Lectures On The Theory Of Algebraic Functions Of One Variable

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Lectures On The Theory Of Algebraic Functions Of One Variable
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Author : Max Deuring
language : en
Publisher: Springer
Release Date : 2006-11-15
Lectures On The Theory Of Algebraic Functions Of One Variable written by Max Deuring and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Algebraic Functions And Projective Curves
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Author : David Goldschmidt
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-04-06
Algebraic Functions And Projective Curves written by David Goldschmidt and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-04-06 with Mathematics categories.
This book grew out of a set of notes for a series of lectures I orginally gave at the Center for Communications Research and then at Princeton University. The motivation was to try to understand the basic facts about algebraic curves without the modern prerequisite machinery of algebraic geometry. Of course, one might well ask if this is a good thing to do. There is no clear answer to this question. In short, we are trading off easier access to the facts against a loss of generality and an impaired understanding of some fundamental ideas. Whether or not this is a useful tradeoff is something you will have to decide for yourself. One of my objectives was to make the exposition as self-contained as possible. Given the choice between a reference and a proof, I usually chose the latter. - though I worked out many of these arguments myself, I think I can con?dently predict that few, if any, of them are novel. I also made an effort to cover some topics that seem to have been somewhat neglected in the expository literature.
Lectures On The Theory Of Algebraic Functions Of One Variable Notes By C P Ramanujam
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Author : Max Deuring
language : en
Publisher:
Release Date :
Lectures On The Theory Of Algebraic Functions Of One Variable Notes By C P Ramanujam written by Max Deuring and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with Algebraic functions categories.
Algebraic Function Fields And Codes
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Author : Henning Stichtenoth
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11
Algebraic Function Fields And Codes written by Henning Stichtenoth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-11 with Mathematics categories.
This book links two subjects: algebraic geometry and coding theory. It uses a novel approach based on the theory of algebraic function fields. Coverage includes the Riemann-Rock theorem, zeta functions and Hasse-Weil's theorem as well as Goppa' s algebraic-geometric codes and other traditional codes. It will be useful to researchers in algebraic geometry and coding theory and computer scientists and engineers in information transmission.
Dynamical Systems Warwick 1974
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Author : A. Manning
language : en
Publisher: Springer
Release Date : 2006-11-15
Dynamical Systems Warwick 1974 written by A. Manning and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Canadian Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1972-10
Canadian Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1972-10 with categories.
Algebraic Geometry In Coding Theory And Cryptography
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Author : Harald Niederreiter
language : en
Publisher: Princeton University Press
Release Date : 2009-09-21
Algebraic Geometry In Coding Theory And Cryptography written by Harald Niederreiter and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-09-21 with Mathematics categories.
This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books
Function Field Arithmetic
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Author : Dinesh S Thakur
language : en
Publisher: World Scientific
Release Date : 2004-06-01
Function Field Arithmetic written by Dinesh S Thakur and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-06-01 with Mathematics categories.
This book provides an exposition of function field arithmetic with emphasis on recent developments concerning Drinfeld modules, the arithmetic of special values of transcendental functions (such as zeta and gamma functions and their interpolations), diophantine approximation and related interesting open problems. While it covers many topics treated in 'Basic Structures of Function Field Arithmetic' by David Goss, it complements that book with the inclusion of recent developments as well as the treatment of new topics such as diophantine approximation, hypergeometric functions, modular forms, transcendence, automata and solitons. There is also new work on multizeta values and log-algebraicity. The author has included numerous worked-out examples. Many open problems, which can serve as good thesis problems, are discussed.
Collected Papers
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Author : Armand Borel
language : en
Publisher: Springer Science & Business Media
Release Date : 1983
Collected Papers written by Armand Borel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
This book collects the papers published by A. Borel from 1983 to 1999. About half of them are research papers, written on his own or in collaboration, on various topics pertaining mainly to algebraic or Lie groups, homogeneous spaces, arithmetic groups (L2-spectrum, automorphic forms, cohomology and covolumes), L2-cohomology of symmetric or locally symmetric spaces, and to the Oppenheim conjecture. Other publications include surveys and personal recollections (of D. Montgomery, Harish-Chandra, and A. Weil), considerations on mathematics in general and several articles of a historical nature: on the School of Mathematics at the Institute for Advanced Study, on N. Bourbaki and on selected aspects of the works of H. Weyl, C. Chevalley, E. Kolchin, J. Leray, and A. Weil. The book concludes with an essay on H. Poincaré and special relativity. Some comments on, and corrections to, a number of papers have also been added.
Codes On Algebraic Curves
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Author : Serguei A. Stepanov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Codes On Algebraic Curves written by Serguei A. Stepanov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This is a self-contained introduction to algebraic curves over finite fields and geometric Goppa codes. There are four main divisions in the book. The first is a brief exposition of basic concepts and facts of the theory of error-correcting codes (Part I). The second is a complete presentation of the theory of algebraic curves, especially the curves defined over finite fields (Part II). The third is a detailed description of the theory of classical modular curves and their reduction modulo a prime number (Part III). The fourth (and basic) is the construction of geometric Goppa codes and the production of asymptotically good linear codes coming from algebraic curves over finite fields (Part IV). The theory of geometric Goppa codes is a fascinating topic where two extremes meet: the highly abstract and deep theory of algebraic (specifically modular) curves over finite fields and the very concrete problems in the engineering of information transmission. At the present time there are two essentially different ways to produce asymptotically good codes coming from algebraic curves over a finite field with an extremely large number of rational points. The first way, developed by M. A. Tsfasman, S. G. Vladut and Th. Zink [210], is rather difficult and assumes a serious acquaintance with the theory of modular curves and their reduction modulo a prime number. The second way, proposed recently by A.